HELP: Mesh Gaps & Bone Properties
With the sharp edges/splits, it looks like the problem is that you are using an edge split modifier, and it is above your armature modifier in the modifier stack. Try using the up/down arrow buttons in the top right corner of the modifier to move the edge split modifier below the armature modifier.

As for the hand bones, I don't know enough about the export process here (are you using fbx or some other format?), but the bones may exist on a different bone layer in the armature. You could try looking through each layer under the armature tab of the object properties (the tab with the symbol that looks like a little man) by clicking on layers to toggle their visibility. 

The other alternative is that the bones may have been hidden using ctrl-h or similar. You can unhide everything in a particular mode (armature edit mode in this case) by using alt-h.